On a Control to Pump a Swing

The problem of pumping a swing by a human standing or sitting on it is studied. For the both cases, we try to design a control that maximizes the height of the swing at the end of each semi-oscillation. Such control is searched for in the feedback form. The viscous friction in the suspension joint is taken into account. Under the optimal control, swing tends to a self-sustained regime of motion. It can be either oscillatory or rotation motion depending on friction coefficient and other parameters of the system.